Failure Probability Estimation of Wind Turbines by Enhanced Monte Carlo Method
Publication: Journal of Engineering Mechanics
Volume 138, Issue 4
Abstract
This paper discusses the estimation of the failure probability of wind turbines required by codes of practice for designing them. The Standard Monte Carlo (SMC) simulations may be used for this reason conceptually as an alternative to the popular Peaks-Over-Threshold (POT) method. However, estimation of very low failure probabilities with SMC simulations leads to unacceptably high computational costs. In this study, an Enhanced Monte Carlo (EMC) method is proposed that overcomes this obstacle. The method has advantages over both POT and SMC in terms of its low computational cost and accuracy. The method is applied to a low-order numerical model of a 5 MW wind turbine with a pitch controller exposed to a turbulent inflow. Two cases of the wind turbine model are investigated. In the first case, the rotor is running with a constant rotational speed. In the second case, the variable rotational speed is controlled by the pitch controller. This provides a fair framework for comparison of the behavior and failure event of the wind turbine with emphasis on the effect of the pitch controller. The Enhanced Monte Carlo method is then applied to the model and the failure probabilities of the model are estimated to the values related to the required 50-year return period of the wind turbine.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The Danish Energy Authority is acknowledged for their support under grant EFP07-II, Estimation of Extreme Responses and Failure Probability of Wind Turbines under Normal Operation by Controlled Monte Carlo Simulation.
The financial support from the Research Council of Norway (NFR) through the Centre for Ships and Ocean Structures (CeSOS) at the Norwegian University of Science and Technology is also gratefully acknowledged.
References
Cook, N. J., and Harris, R. I. (2004). “Exact and general FT1 penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents.” Struct. Saf., 26(4), 391–420.
Freudenreich, K., and Argyriadis, K. (2007). “The load level of modern wind turbines according to IEC 61400-1.” J. Phys. Conf. Ser., 75(012075), 1–11.
Hansen, M. (2007). Aerodynamics of wind turbines, 2nd Ed., Earthscan, Oxford, U.K.
Harris, I. (2005). “Generalised pareto methods for wind extremes. Useful tool or mathematical mirage?.” J. Wind Eng. Ind. Aerodyn., 93(5), 341–360.
Harris, R. I. (2004). “Extreme value analysis of epoch maximaconvergence, and choice of asymptote.” J. Wind Eng. Ind. Aerodyn., 92(11), 897–918.
International Electrotechnical Commission (IEC). (2005a). Amendment to the IEC 61400-1:2005 standard, Geneva, Switzerland.
International Electrotechnical Commission (IEC). (2005b). Wind turbines—Part 1: Design requirements, IEC 61400-1, 3rd Ed., Geneva, Switzerland.
Jonkman, J., Butterfield, S., Musial, W., and Scott, G.,(2009). “Definition of a 5-MW reference wind turbine for offshore system development.” Report No. NREL/TP-500-38060, National Renewable Energy Laboratory, Golden, CO.
Katafygiotis, L., and Zuev, K. (2008). “Geometric insight into the challenges of solving high-dimensional reliability problems.” Prob. Eng. Mech., 23(2–3), 208–218.
Kooijman, H., Lindenburg, C., Winkelaar, D., and van der Hooft, E. (2003). “Aero-elastic modelling of the dowec 6 MW pre-design in PHATAS.” Report No. DOWEC 10046 009, ECN-CX01-135, Energy Research Center of the Netherlands, Petten, Netherlands.
Macke, M., and Bucher, C. (2003). “Importance sampling for randomly excited dynamical systems.” J. Sound Vib., 268(2), 269–290.
Meirovitch, L. (2001). Fundamentals of vibrations, McGraw-Hill, New York.
Naess, A., and Gaidai, O. (2008a). “A Monte Carlo approach to prediction of extreme response statistics of drag dominated offshore structures.” J. Offshore Mech. Arct. Eng., 130(4), 041601.
Naess, A., and Gaidai, O. (2008b). “Monte Carlo methods for estimating the extreme response of dynamical systems.”J. Eng. Mech., 134(8), 628–636.
Naess, A., and Gaidai, O. (2009). “Estimation of extreme values from sampled time series.” Struct. Saf., 31(4), 325–334.
Naess, A., Gaidai, O., and Batsevych, O. (2010). “Prediction of extreme response statistics of narrow-band random vibrations.” J. Eng. Mech., 136(3), 290–298.
Naess, A., Leira, B., and Batsevych, O. (2009). “System reliability analysis by enhanced Monte Carlo simulation.” Struct. Saf., 31(5), 349–355.
Ogata, K. (2009). Modern Control Engineering, 5th Ed., Prentice Hall, Upper Saddle River, NJ.
Pradlwarter, H. J., and Schuëller, G. I. (2010). “Local domain Monte Carlo simulation.” Struct. Saf., 32(5), 275–280.
Pradlwarter, H., Schuëller, G., Koutsourelakis, P., and Charmpis, D. (2007). “Application of line sampling simulation method to reliability benchmark problems.” Struct. Saf., 29(3), 208–221.
Schuëller, G. (2008). “Computational stochastic dynamics—some lessons learned.” Chapters 1, 320, Computational Structural Dynamics and Earthquake Engineering, Vol. 2, Structures & Infrastructures Series, Taylor & Francis, New York.
Sichani, M. T., Pedersen, B. J., and Nielsen, S. R. K. (2009). “Stochastic subspace modeling of turbulence.” World Academy of Science, Engineering and Technology, 58, 323–331.
Sichani, M. T., Nielsen, S. R. K., and Bucher, C. (2011). “Efficient estimation of first passage probability of high dimensional non-linear systems.” Probab. Eng. Mech., in press.
Simiu, E., Heckert, N. A., Filliben, J. J., and Johnson, S. K. (2001). “Extreme wind load estimates based on the gumbel distribution of dynamic pressures: an assessment.” Struct. Saf., 23(3), 221–229.
Valdebenito, M., Pradlwarter, H., and Schuëller, G. (2010). “The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities.” Struct. Saf., 32(2), 101–111.
Xue, D., Chen, Y., and Atherton, D. (2008). “Linear feedback control: Analysis and Design with MATLAB”. Society for Industrial and Applied Mathematics (SIAM).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 4 • April 2012
Pages: 379 - 389
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Jan 3, 2011
Accepted: Sep 2, 2011
Published online: Sep 5, 2011
Published in print: Apr 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.